OBs should never make 'predictions' like this. They have absolutely no idea when you will go. Such a stupid thing to say to a pregnant mama, unless they're hoping you'll get discouraged near the end now and 'suggest' you get an induction. I'd be weary.
I just had my 36/37 week appointment and when I told my OB that I would see him in a week, he made a comment "maybe sooner!" - I honestly think it was just to make the point that you really have no idea. There really is no way to predict - even between pregnancies for the same woman (a friend of mine was late with her first and two weeks early with her second). Your due date is an estimate - anyone could go 2 weeks before or 2 weeks after and it would be considered normal. I think it's actually kind of mean for an OB to say this without acknowledging the "or you'll be late" possibility - as you get antsy towards the end you're going to be even more hopeful for a slightly early delivery date now that your OB has put this in your head. Plan for early but mentally gear up for late - that way you'll be ready no matter when you go and with the least amount of frustration. Good luck!
Delivering at 38/39 weeks is totally normal, just like 40/41 weeks. So, er, yeah, we're all in that same boat. I guess I don't even understand why you doctor would mention that.
Re: Take what OB says with a grain of salt
2nd round exp 8/20/18.